How Do We Know Anything? Hume, Popper, Kuhn and the Problem of Science

Follows: Epistemology: How Do We Know What Is Actually True? and The Allegory of the Cave

In this deep dive
1. Hume's bombshell: why the sun rising tomorrow can't be proved
2. Logical positivism: the attempt to make meaning scientific, and why it fell apart
3. Popper: science as bold guesses and failed refutations
4. Kuhn: paradigms, puzzles and revolutions
5. Lakatos and Feyerabend: rescuing method, and abandoning it
6. Bayes: confirmation as degrees of belief
7. The replication crisis: the whole debate, live

Part 1 — Hume's bombshell

The Allegory of the Cave asked how we could ever tell shadows from reality. Epistemology introduced the classic definition of knowledge as justified true belief, and mentioned in passing that David Hume showed "even scientific induction relies on an unprovable assumption: that the future will resemble the past." That passing mention is one of the most important ideas in the history of thought. This piece starts there, and follows it all the way to a crisis in modern laboratories.

Two kinds of knowledge

In An Enquiry Concerning Human Understanding (1748, Section IV), Hume divides everything we can know into two kinds. Relations of ideas are truths like those of mathematics: that three times five is half of thirty. You can know them by thought alone, and denying them produces a contradiction. Matters of fact are claims about the world, and they're different. Their opposite is always conceivable. "That the sun will not rise to-morrow," Hume writes, "is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise."

So how do we know matters of fact we haven't observed? Through cause and effect, Hume says. And how do we know causes? Only through experience: we've seen bread nourish us, fire burn, one billiard ball move another.

The step nobody can justify

Here's the bombshell. "The bread, which I formerly eat, nourished me," Hume writes, but "does it follow, that other bread must also nourish me at another time?" There's a gap between I have found that such an object has always been attended with such an effect and I foresee that similar objects will be attended with similar effects. The step isn't a logical deduction, since nothing contradictory follows from denying it. Could it be justified by experience? No, because "all inferences from experience suppose, as their foundation, that the future will resemble the past." Using past experience to prove that past experience is a reliable guide goes in a circle.

This is the problem of induction. It first appeared in Hume's Treatise of Human Nature (1739); the Enquiry gives a shorter version. Notice what Hume is not saying. He doesn't say we should stop expecting bread to nourish us. He says that our expectation isn't the product of reasoning at all.

Custom, the great guide

What produces the expectation, then? Habit. "Custom, then, is the great guide of human life. It is that principle alone which renders our experience useful to us" (Section V). We expect the future to resemble the past because we're the kind of creatures who form such expectations, not because we've proved anything.

Bertrand Russell gave the problem its most memorable mascot in The Problems of Philosophy (1912): "The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken." The chicken's evidence was excellent, right up to the last day.

Every scientific law is a bet that the future will behave like the past. Hume showed that the bet can't be proved to be a good one without assuming it already is.

A newer riddle

In 1955 Nelson Goodman made things worse with a "new riddle of induction." Define a word, "grue": an object is grue if it's green and observed before some future time t, or blue otherwise. Every emerald ever examined is green. But every emerald examined so far is also grue. So the evidence supports "all emeralds are green" and "all emeralds are grue" equally, and the two predict different colours after time t. Why is one a natural projection and the other absurd? Goodman's point: induction isn't just "extend the pattern." We need some account of which patterns are worth extending, and logic alone doesn't supply it.

Philosophers have tried many escape routes. Hans Reichenbach offered a "pragmatic vindication": if any method of predicting works, induction will. P. F. Strawson argued that asking for a justification of induction as a whole is a confused demand. None has satisfied everyone. The rest of this piece is, in a sense, the story of how philosophers of science tried to build a theory of scientific knowledge on top of a foundation Hume had cracked.

Part 2 — Logical positivism: making meaning scientific

The Vienna Circle

Between 1924 and 1936, a group of philosophers and scientists met regularly in Vienna under the nominal leadership of Moritz Schlick. They became known as the Vienna Circle, and their 1929 unofficial manifesto, "The Scientific World Conception," was signed by Rudolf Carnap, Hans Hahn and Otto Neurath. Their movement, logical positivism (or logical empiricism), wanted philosophy to be as rigorous as physics.

They took a cue from the end of Hume's Enquiry, a passage that still startles. Pick up any book of theology or metaphysics, Hume says, and ask: "Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion."

The verification principle

The positivists turned Hume's fork into a test of meaning. A statement is meaningful, they said, only if it's either true by definition (like logic and mathematics) or verifiable in principle by experience. "Water boils at 100 °C at sea level" is meaningful. "The Absolute is beyond time" isn't false. It's literally nonsense, because no observation could ever bear on it. A. J. Ayer brought the idea to English readers in Language, Truth and Logic (1936).

It was an exhilarating idea. Whole libraries of metaphysics could be cleared away, and philosophy could become the clarifier of science.

Why it fell apart

The trouble came quickly, and much of it from inside the Circle itself.

1. Universal laws can't be verified. "All metals expand when heated" covers infinitely many cases, so no finite set of observations can verify it. By the strict criterion, the laws of science would be meaningless. Carnap responded in 1936 by weakening the criterion to mere confirmability, partial testability, and the attempts to state that precisely ran into one technical problem after another.
2. The principle seemed to refute itself. "Only verifiable or analytic statements are meaningful" isn't obviously verifiable or analytic. The SEP's entry on logical empiricism notes this charge "sounds more compelling than it is": Ayer treated the principle as a definition, a proposal about how to use the word "meaning." But then critics could simply decline the proposal.
3. Quine's holism. In "Two Dogmas of Empiricism" (1951), W. V. O. Quine attacked the sharp line between analytic and empirical truths and argued that statements don't face experience one at a time. They face it as a whole web, so no individual sentence has its own neat set of verifying observations.

History intervened too. The Circle was scattered by emigration and exile in the 1930s, and Schlick was murdered in 1936. In 1967, the philosopher John Passmore wrote the famous obituary: "Logical positivism, then, is dead, or as dead as a philosophical movement ever becomes."

Logical positivism died, but its question didn't: what makes a claim scientific, rather than just confident-sounding?

The obituary was partly premature. The SEP's entry on the Vienna Circle notes that while some of its doctrines may be "as dead as philosophies can be," others "show signs of surprising vitality," and that which ones is still debated. Its demand for clarity, its respect for logic and its insistence that claims about the world answer to evidence shaped all the philosophy of science that followed, including its fiercest critics.

Part 3 — Popper: bold guesses and failed refutations

Four theories in Vienna

Karl Popper was born in Vienna in 1902. His lifelong concern with what makes a theory scientific overlapped with the Circle's, though his answer was very different. As a young man around 1919 he encountered four big theories: Marx's theory of history, Freud's psychoanalysis, Alfred Adler's individual psychology, and Einstein's general relativity.

What struck him was a difference in attitude. As the SEP summarises it, "The dominance of the critical spirit in Einstein, and its total absence in Marx, Freud and Adler, struck Popper as being of fundamental importance." Marxists and psychoanalysts saw confirmations everywhere. Any behaviour at all could be interpreted to fit their theory. Einstein's theory, in contrast, stuck its neck out. It predicted that light passing near the Sun would be bent by a specific amount, an outcome that, given Newtonian physics, was highly improbable. Eddington's eclipse observations in 1919 tested the prediction, and if it had failed, the theory would have been in serious trouble. Psychoanalytic theories, Popper later wrote in Conjectures and Refutations (1963), were "simply non-testable, irrefutable. There was no conceivable human behaviour which could contradict them."

Falsifiability

From this, Popper built a new answer to Hume and a new criterion for science. In Logik der Forschung (1935; English as The Logic of Scientific Discovery, 1959) he accepted that Hume was right: induction can't be justified. But, he argued, science doesn't actually need it.

The key is a logical asymmetry. No number of white swans proves "all swans are white." But a single black swan refutes it. Verification is impossible; falsification is possible. So science, on Popper's view, works by conjecture and refutation: propose bold hypotheses, deduce risky predictions, and try hard to knock them down. A theory that survives severe tests is corroborated, but never proved. It remains our best guess until something kills it.

This gives a demarcation criterion: a theory is scientific if it's falsifiable, if there's some possible observation that would show it false. Popper wasn't saying unfalsifiable ideas are meaningless, as the positivists had. Metaphysics could be meaningful and even inspire science. It just isn't science.

He applied the criterion with a political edge. Marxism, he argued, had started out scientific, since it made genuine predictions. When those failed, its defenders added ad hoc hypotheses to save it, and so a scientific theory degenerated into dogma.

What Popper got right is hard to overstate. He turned the scientific attitude into something you can check: does this claim forbid anything? He also explained why piling up confirmations is cheap. It is, he argued, easy to obtain evidence in favour of virtually any theory, so confirmations should count only when they come from predictions that might really have failed.

A good scientific theory tells you, in advance, what would prove it wrong.

The problems

Falsifiability is a powerful idea, and philosophers found serious problems with it as a complete account of science:

1. No hypothesis is tested alone. Pierre Duhem had already argued that when a prediction fails, "not only is the questioned proposition put into doubt, but also the whole theoretical scaffolding used by the physicist." A failed prediction tells you that something in your package of theory, auxiliary assumptions and instruments is wrong, not which part. Quine generalised the point. Logic alone never forces you to abandon the theory rather than an assumption.
2. Scientists rightly ignore refutations. For decades, Mercury's orbit didn't quite fit Newtonian mechanics. Astronomers didn't abandon Newton; they looked for unseen bodies and kept working, until Einstein's theory came along. By strict Popperian standards, they should have treated Newton as refuted. Most people think they were right not to.
3. Probabilistic claims can't be falsified by single cases. "Smoking raises the risk of cancer" isn't refuted by a smoker who lives to 95.
4. Corroboration sounds like induction in disguise. If a theory's surviving tests gives us no reason to expect it to keep surviving, why rely on it to build bridges? Critics argue that Popper's view needs a little induction after all.

Part 4 — Kuhn: paradigms, puzzles and revolutions

A historian looks at science

Thomas Kuhn (1922–1996) began in physics, graduating from Harvard in 1943, then switched to the history of science, and eventually to philosophy. In 1965 an international colloquium at Bedford College, London, set up a now-famous confrontation between his ideas and Popper's; the papers, with contributions from Lakatos and Feyerabend, became the book Criticism and the Growth of Knowledge (1970). His The Structure of Scientific Revolutions (1962) is, the SEP says, "one of the most cited academic books of all time," and it gave the world the word paradigm in its modern sense.

Kuhn's complaint was that philosophers described science as it ought to be, while history showed something different. Real science, he argued, moves in a cycle:

Normal science → Anomalies → Crisis → Revolution → New normal science

1. Normal science. A mature field works within a paradigm: a shared framework of theory, methods, instruments, standards and model examples. The paradigm supplies the puzzles and the tools to solve them. Most scientists, most of the time, aren't testing their foundations at all, Popper notwithstanding. They're solving puzzles the paradigm says are solvable.
2. Anomalies. Some puzzles resist solution. At first they're set aside as problems for later.
3. Crisis. When anomalies pile up, or one becomes impossible to ignore, confidence in the paradigm erodes.
4. Revolution. A rival paradigm emerges, and the field eventually switches. Kuhn compared the switch to a gestalt shift, like the famous drawing that flips from a duck to a rabbit. After it, scientists see the same data differently.

Before writing Structure, Kuhn had published The Copernican Revolution (1957), and the move from an Earth-centred to a Sun-centred astronomy is the classic illustration.

Incommensurability

Kuhn's most controversial claim was that rival paradigms can be incommensurable: they lack a common measure. Their key terms shift in meaning ("mass" in Newton and Einstein are not quite the same concept), they rank problems differently, and their defenders disagree about what counts as a good solution. So a paradigm switch can't be settled by a neutral algorithm.

Critics heard this as a claim that science is irrational, or decided by fashion. The SEP notes that Kuhn's rejection of rules for theory choice "appeared tantamount to the claim that science is irrational."

Kuhn didn't say science is irrational. He said scientific rationality looks more like trained judgement than like following an algorithm.

Kuhn's clarifications

Kuhn spent much of his later career saying he'd been misread. The philosopher Margaret Masterman pointed out in 1970 that he had used "paradigm" in a wide variety of senses. In the postscript to the 1970 second edition, Kuhn separated two of them: the disciplinary matrix, the whole constellation of a community's shared commitments, and the exemplar, the concrete model solution that students learn from and imitate.

In a 1977 essay he also named five values that scientists share when choosing between theories: accuracy, consistency, scope, simplicity and fruitfulness. Everyone uses them, but they can pull in different directions and be weighted differently, which is why reasonable scientists can disagree during a revolution without anyone being irrational.

What Kuhn got right, and what's still argued

Kuhn's lasting contribution was to make science's social structure part of its epistemology. Science is done by communities with training, shared exemplars, incentives and institutions. Whether that structure makes science more reliable or less, and under what conditions, is a question you'll meet again in Part 7. His incommensurability thesis remains contested. Most philosophers think rival theories can be compared more than Kuhn's strongest statements allowed, but that theory choice involves judgement, not just logic.

Part 5 — Lakatos and Feyerabend: rescuing method, and abandoning it

Lakatos: research programmes

Imre Lakatos (1922–1974) fled Hungary in 1956 after the Soviet suppression of the uprising. He had been taught by Popper at the London School of Economics, rose to become its Professor of Logic, and produced what the SEP calls a "radical revision" of Popper's demarcation criterion. He wanted to keep Popper's rationality while accepting Kuhn's history. His solution, set out in "Falsification and the Methodology of Scientific Research Programmes" (1970), changed the unit of evaluation from a single theory to a research programme: a sequence of theories sharing a common core.

When a prediction fails, scientists modify the belt, not the core. That's legitimate, Lakatos said, but there's a test of whether it's going well. A programme is progressive if its modifications predict novel facts that turn out true. It's degenerating if it only patches up failures after the fact. In his words, a research programme "is progressive if it is both theoretically and empirically progressive, and degenerating if it is not."

The history of Uranus is a vivid illustration of the progressive kind. Uranus's orbit didn't match Newtonian predictions. Instead of abandoning Newton, the French mathematician Urbain Le Verrier adjusted the belt: he proposed an unseen planet and calculated its position. Johann Galle at the Berlin Observatory found Neptune in 1846 on his first night of searching. The anomaly became a triumph. Mercury's anomaly, by contrast, resisted such patching for decades, and the programme was eventually overtaken by Einstein's.

A common objection is that there's no deadline. A degenerating programme might recover, so the method seems better at grading programmes than at telling you when to quit. Feyerabend went further: he argued that Lakatos's methodology either rests on "ungrounded value judgments" about good science or is "epistemological anarchism in disguise."

Feyerabend: against method

Paul Feyerabend (1924–1994) was Lakatos's friend and sparring partner. They planned a joint book, For and Against Method. After Lakatos died in 1974, Feyerabend's half became Against Method (1975), one of the most provocative books in the field.

His argument was historical. Look closely at great episodes of science, he said, and you find that the heroes broke every rule philosophers have proposed. He portrayed Galileo as using rhetoric, propaganda and epistemological tricks to win support for the Sun-centred system, at a time when Aristotle's physics had strong empirical arguments on its side. If Galileo had obeyed the methodologists, science would not have progressed.

Hence the notorious slogan, "anything goes." It's widely misread as "all ideas are equally good." Feyerabend's point, as the SEP explains, was narrower: if you insist on a universal methodology that never inhibits progress, the only rule it can contain is the useless one, "anything goes." In other words, every methodological rule has limited validity. Feyerabend did go further in later work. He defended the pursuit of alternative medicine and astrology and attacked the authority of science in public life, which made him a hero to some and a villain to others.

Feyerabend's real target wasn't science. It was the belief that science owes its success to one method you could write down.

Part 6 — Bayes: confirmation as degrees of belief

The idea in one paragraph

A different tradition sidesteps the debate over refutation by treating belief as a matter of degree. On the Bayesian view, evidence confirms a hypothesis when it makes the hypothesis more probable than it was before, and how much it does so depends on how much more likely the evidence is if the hypothesis is true than if it's false. This library already teaches the machinery. The Mathematics piece Bayes' Theorem: What a Positive Test Really Means builds it with a 1,000-person calculator, and Bayesian Thinking for Everyday Life, in Thinking & Learning, turns it into a habit. Here the question is what it does for the philosophy of science.

It explains what Popper got right

Bayes vindicates the power of risky predictions. Suppose a theory starts with a 10% chance of being right. It predicts something that would happen 95% of the time if it's true.

The risky prediction moves the theory from 10% to about 68%. The safe prediction barely moves it at all. That's Popper's insight, recovered without his ban on induction: a theory that "explains everything," whose predictions would come true anyway, gains nothing from its successes.

Bayesians argue it also helps with Duhem's problem. When a prediction fails, the probabilities flow back through the whole package, and the part that loses most credibility tends to be the one you were least sure of to begin with. That fits what astronomers did with Uranus: they doubted the assumption that there were no more planets, not Newton.

What it doesn't solve

1. The problem of the priors. Where do the starting probabilities come from? "Subjective" Bayesians allow any coherent prior; "objective" Bayesians look for rules that narrow the choice. Subjectivists point to merging-of-opinions theorems, which show that under certain conditions people with different priors should expect their beliefs to converge as shared evidence piles up, though only in the long run. The SEP's entry on Bayesian epistemology gives a telling example. You observe a hundred black ravens. Should your confidence that the next raven is black go up? It depends entirely on your prior distribution. With some priors, credence rises; with others, it stays put or even falls. Hume's problem hasn't been solved; it has moved into the choice of priors.
2. Old evidence. In 1915, Einstein showed that general relativity explained the anomaly in Mercury's orbit, a fact known for over fifty years. That rightly raised confidence in the theory. But on the simplest Bayesian account, evidence you already know can't raise any probability, because you already had it. Clark Glymour pressed this problem in 1980, and it's still debated.
3. The ravens paradox. Carl Hempel noticed in 1945 that "all ravens are black" is logically equivalent to "all non-black things are non-ravens." So a green apple seems to confirm that all ravens are black. Bayesian analyses can separate the cases: given plausible background assumptions (for instance, that the number of ravens doesn't depend on their colour), a black raven confirms the hypothesis and a green apple doesn't. But the result hangs on those assumptions, and the literature on getting them right is still growing.

Part 7 — The replication crisis: the whole debate, live

What happened

In 2011, the Journal of Personality and Social Psychology, one of the field's top journals, published a paper by Daryl Bem reporting experimental evidence for precognition, or ESP. It had passed standard peer review. Three independent attempts to replicate it failed, and the journal that published the original declined to publish the replications, on the grounds that they weren't new research. They eventually appeared in PLoS ONE in 2012. The SEP's entry on reproducibility describes the Bem episode as one common origin story of psychology's "replication crisis."

The same year, Joseph Simmons, Leif Nelson and Uri Simonsohn showed in Psychological Science that undisclosed flexibility in collecting and analysing data "dramatically increases actual false-positive rates." In many cases, they wrote, a researcher is more likely to find evidence for an effect that doesn't exist than to correctly find that it doesn't.

Then came the large-scale checks:

A Nature poll of about 1,500 researchers in 2016 found that more than half (52%) believed science was facing a reproducibility crisis.

Every philosopher in this piece saw part of it coming

This is where the abstract debate becomes concrete. Each idea above explains part of what went wrong.

• Hume. Every published result is an inductive leap from a sample to the world. Small samples are short runs of evidence, like the chicken's. The SEP notes that direct replications make up roughly 1% of the published psychology literature, so most leaps were never checked.
• Popper. Flexibility in analysis is the ad hoc rescue of the twenty-first century. If you can choose, after seeing the data, which outcomes to report, which participants to exclude and when to stop collecting, your hypothesis can't fail. It has become unfalsifiable without anyone deciding to make it so.
• Kuhn. Science is a social practice with incentives. The SEP documents journals that historically refused to publish replications, and a "publish or perish" culture that rewards novel, positive, surprising results. The community's shared standards, its paradigm of good practice, were part of the problem.
• Lakatos. A research programme that answers each failed replication by adding a new condition or moderator, without ever predicting anything new that turns out true, fits his definition of degeneration exactly.
• Bayes. In 2005 John Ioannidis published "Why Most Published Research Findings Are False" in PLoS Medicine. His argument is Bayesian at heart: the chance that a "significant" finding is true depends on how plausible the hypothesis was to begin with, the study's statistical power, and the amount of bias.

Here's his logic with illustrative numbers (computed from the formula in Ioannidis's paper, not data from any particular field). Imagine 1,000 hypotheses tested, of which 200 are actually true.

Nothing in the bottom row requires fraud. Small samples and flexible analysis are enough to turn a literature mostly false.

The replication crisis wasn't science failing. It was science's own methods, finally turned on itself, finding the failure.

What changed

The response has been, in a sense, applied philosophy of science. Reformers proposed pre-registration, publicly recording your hypothesis and analysis plan before collecting data, which is falsifiability made enforceable. In 2013 the journal Cortex launched Registered Reports, in which peer review happens before the results exist, and a study that passes gets an in-principle acceptance that can't be revoked because of what it finds. Data sharing, larger samples, and replication studies have become far more common, and new fields of "meta-science" study science itself. Vazire (2018) has called this a "credibility revolution," and in 2018 Nelson, Simmons and Simonsohn argued that experimental psychology's practices "have improved dramatically."

A note of caution in both directions. Replication rates vary a lot by field and method, and the projects above sampled particular journals and kinds of study. A failed replication, as the cancer biology team put it, "does not disconfirm a finding, but it does suggest that additional investigation is needed." The crisis is a reason to trust single, surprising studies less. It is not a reason to distrust well-replicated science, such as the effectiveness of vaccines or the physics that keeps planes in the air.

So how should you trust science?

Putting the whole story together suggests a practical stance:

1. Trust convergence, not single results. One study is a conjecture. Many independent studies, by different teams with different methods, are something close to knowledge.
2. Prefer risky predictions. Ask whether the claim was stated in advance, in a way that could have failed.
3. Weigh prior plausibility. A surprising result in a small study is, by Bayes, more likely to be a false positive. Extraordinary claims need extraordinary evidence.
4. Look for the self-correction. The best evidence that a field is healthy isn't that it's never wrong. It's that it publishes its replications, shares its data and changes its practices when it finds out.

The takeaway

Hume showed that no amount of past evidence logically guarantees the future, and that our reliance on induction is a habit, not a proof. The logical positivists tried to make meaning itself depend on verification, and collapsed under their own criterion. Popper replaced verification with falsification: science advances by bold conjectures that survive attempts to refute them. Kuhn showed that real science runs on shared paradigms and changes through revolutions that involve judgement, not algorithms. Lakatos judged research programmes by whether they predict new facts, and Feyerabend argued that no single method explains science's success. Bayesian confirmation unites several of these insights but moves Hume's problem into the choice of priors. The replication crisis shows all of them at work: small samples, unfalsifiable flexibility, bad incentives and low priors produced a literature full of false positives, and science's own methods found and began to fix it. Trust science the way it deserves to be trusted: in proportion to replication, risk and convergence.

Try this: pick a scientific claim you've seen in the news this month, and ask four questions. Popper: what result would have shown it false, and was that stated in advance? Bayes: how plausible was it before this study? Hume: how big was the sample, and has anyone else found the same thing? Kuhn: who funded or rewarded this result, and what would the field lose if it turned out wrong? Write down your confidence before and after. That's the whole history of the philosophy of science, in ten minutes.

Sources & Further Reading

Sources
- David Hume, An Enquiry Concerning Human Understanding (1748), Sections IV, V and XII (Project Gutenberg); SEP, "The Problem of Induction" (Treatise 1739; Goodman's grue; Reichenbach; Strawson).
- Bertrand Russell, The Problems of Philosophy (1912), ch. 6 (Project Gutenberg).
- SEP, "Vienna Circle" (dates, manifesto, Schlick's murder, Passmore's "as dead as"); SEP, "Logical Empiricism" (Passmore 1967 quotation; the self-undercutting charge; Quine 1951).
- SEP, "Karl Popper" (1919, Eddington, Logik der Forschung 1935, Conjectures and Refutations 1963 quotation, Marxism and ad hoc hypotheses); SEP, "Pierre Duhem" (Duhem's thesis quotation).
- SEP, "Thomas Kuhn" (Structure 1962; paradigms; Masterman 1970; 1970 postscript; five values, 1977).
- SEP, "Imre Lakatos" (research programmes; hard core and protective belt; Mercury); NASA, "Neptune: Facts" (Le Verrier and Galle, 1846). SEP, "Paul Feyerabend" (Against Method; "anything goes"; Galileo).
- SEP, "Bayesian Epistemology" (priors; ravens example; old evidence and Glymour 1980); SEP, "Confirmation" and "Carl Hempel" (ravens paradox). Bayes table computed by the author.
- SEP, "Reproducibility of Scientific Results" (Bem 2011; replication about 1% of psychology literature; publication bias; "credibility revolution"). Open Science Collaboration, Science 349 (2015), abstract via PubMed; Begley & Ellis, Nature 483 (2012); Camerer et al., Nature Human Behaviour 2 (2018); Errington et al., eLife (2021); Baker, Nature 533 (2016); Simmons, Nelson & Simonsohn, Psychological Science (2011); Nelson, Simmons & Simonsohn, Annual Review of Psychology (2018); Ioannidis, PLoS Medicine (2005), PPV formula; Chambers, Cortex (2013). Ioannidis table computed by the author from his formula.

Go deeper
- 📘 What Is This Thing Called Science? — Alan Chalmers. The classic, clear introduction to induction, Popper, Kuhn, Lakatos, Feyerabend and Bayesianism.
- 📘 The Structure of Scientific Revolutions — Thomas Kuhn (1962). Short, readable and still provocative. Read the postscript too, where Kuhn answers his critics.
- 📘 Conjectures and Refutations — Karl Popper (1963). The first chapter tells the Vienna story of Einstein, Freud and Marx in Popper's own words.
- 📘 Science Fictions — Stuart Ritchie (2020). A lively account of the replication crisis, bias, hype and the reform movement, aimed at general readers.
- 🌐 Stanford Encyclopedia of Philosophy — The Problem of Induction. Hume's argument and every serious attempt to answer it.
- 🌐 Stanford Encyclopedia of Philosophy — Reproducibility of Scientific Results. The philosophy behind Part 7, with full references.

For Your Vocabulary

Problem of induction (Hume's point that no argument can justify expecting the future to resemble the past without assuming it) · Verification principle (the positivist claim that a statement is meaningful only if analytic or empirically verifiable) · Falsifiability (Popper's test: a scientific theory must rule out some possible observation) · Corroboration (Popper's term for surviving severe tests, short of proof) · Paradigm (Kuhn: a field's shared framework of theory, methods and model solutions) · Incommensurability (Kuhn: rival paradigms lack a fully common measure) · Research programme (Lakatos: a series of theories sharing a hard core, judged by whether they predict novel facts) · Prior probability (how plausible a hypothesis is before the new evidence) · Replication (repeating a study to see if its result holds) · Pre-registration (publicly recording hypotheses and analysis plans before collecting data)